Solutions
Solutions to Try Its
1. [latex]x=-5[/latex] 2. [latex]x=-3[/latex] 3. [latex]x=\frac{10}{3}[/latex] 4. [latex]x=1[/latex] 5. [latex]x=-\frac{7}{17}[/latex]. Excluded values are [latex]x=-\frac{1}{2}[/latex] and [latex]x=-\frac{1}{3}[/latex]. 6. [latex]x=\frac{1}{3}[/latex] 7. [latex]m=-\frac{2}{3}[/latex] 8. [latex]y=4x - 3[/latex] 9. [latex]x+3y=2[/latex] 10. Horizontal line: [latex]y=2[/latex] 11. Parallel lines: equations are written in slope-intercept form.
12. [latex]y=5x+3[/latex]
Solutions to Odd-Numbered Exercises
1. It means they have the same slope. 3. The exponent of the [latex]x[/latex] variable is 1. It is called a first-degree equation. 5. If we insert either value into the equation, they make an expression in the equation undefined (zero in the denominator). 7. [latex]x=2[/latex] 9. [latex]x=\frac{2}{7}[/latex] 11. [latex]x=6[/latex] 13. [latex]x=3[/latex] 15. [latex]x=-14[/latex] 17. [latex]x\ne -4[/latex]; [latex]x=-3[/latex] 19. [latex]x\ne 1[/latex]; when we solve this we get [latex]x=1[/latex], which is excluded, therefore NO solution 21. [latex]x\ne 0[/latex]; [latex]x=\frac{-5}{2}[/latex] 23. [latex]y=\frac{-4}{5}x+\frac{14}{5}[/latex] 25. [latex]y=\frac{-3}{4}x+2[/latex] 27. [latex]y=\frac{1}{2}x+\frac{5}{2}[/latex] 29. [latex]y=-3x - 5[/latex] 31. [latex]y=7[/latex] 33. [latex]y=-4[/latex] 35. [latex]8x+5y=7[/latex] 37. Parallel
39. Perpendicular
41. [latex]m=\frac{-9}{7}[/latex]
43. [latex]m=\frac{3}{2}[/latex]
45. [latex]{m}_{1}=\frac{-1}{3},\text{ }{m}_{2}=3;\text{ }\text{Perpendicular}[/latex]
47. [latex]y=0.245x - 45.662[/latex]. Answers may vary. [latex]{y}_{\text{min}}=-50,\text{ }{y}_{\text{max}}=-40[/latex]
49. [latex]y=-2.333x+6.667[/latex]. Answers may vary. [latex]{y}_{\mathrm{min}}=-10, {y}_{\mathrm{max}}=10[/latex]
51. [latex]y=\frac{-A}{B}x+\frac{C}{B}[/latex]
53. Yes, they are perpendicular.
[latex]\begin{array}{l}\text{The slope for }\left(-1,1\right)\text{ to }\left(0,4\right)\text{ is }3.\\ \text{The slope for }\left(-1,1\right)\text{ to }\left(2,0\right)\text{ is }\frac{-1}{3}.\\ \text{The slope for }\left(2,0\right)\text{ to }\left(3,3\right)\text{ is }3.\\ \text{The slope for }\left(0,4\right)\text{ to }\left(3,3\right)\text{ is }\frac{-1}{3}\end{array}[/latex].
55. 30 ft
57. $57.50
59. 220 mi
